scholarly journals Interior regularity criteria for suitable weak solutions of the magnetohydrodynamic equations

2009 ◽  
Vol 247 (8) ◽  
pp. 2310-2330 ◽  
Author(s):  
Kyungkeun Kang ◽  
Jihoon Lee
Keyword(s):  
Weak Solutions ◽  
Regularity Criteria ◽  
Magnetohydrodynamic Equations ◽  
Suitable Weak Solutions ◽  
Interior Regularity

scholarly journals Partial regularity of suitable weak solutions to the multi-dimensional generalized magnetohydrodynamics equations

2016 ◽  
Vol 18 (06) ◽  
pp. 1650018 ◽  
Author(s):  
Wei Ren ◽  
Yanqing Wang ◽  
Gang Wu
Keyword(s):  
Weak Solutions ◽  
Partial Regularity ◽  
Morrey Space ◽  
Stokes Equations ◽  
Mhd Equations ◽  
Regularity Criteria ◽  
Navier Stokes ◽  
Mixed Norm ◽  
Suitable Weak Solutions ◽  
Navier Stokes Equations

In this paper, we are concerned with the partial regularity of the suitable weak solutions to the fractional MHD equations in [Formula: see text] for [Formula: see text]. In comparison with the work of the 3D fractional Navier–Stokes equations obtained by Tang and Yu in [Partial regularity of suitable weak solutions to the fractional Navier–Stokes equations, Comm. Math. Phys. 334 (2015) 1455–1482], our results include their endpoint case [Formula: see text] and the external force belongs to a more general parabolic Morrey space. Moreover, we prove some interior regularity criteria just via the scaled mixed norm of the velocity for the suitable weak solutions to the fractional MHD equations.

scholarly journals A New Regularity Criterion for the Three-Dimensional Incompressible Magnetohydrodynamic Equations in the Besov Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
TianLi LI ◽  
Wen Wang ◽  
Lei Liu
Keyword(s):  
Weak Solution ◽  
Weak Solutions ◽  
Besov Spaces ◽  
Pressure Field ◽  
Three Dimensional ◽  
Regularity Criterion ◽  
Mhd Equations ◽  
Regularity Criteria ◽  
Magnetohydrodynamic Equations ◽  
Incompressible Magnetohydrodynamic Equations

Regularity criteria of the weak solutions to the three-dimensional (3D) incompressible magnetohydrodynamic (MHD) equations are discussed. Our results imply that the scalar pressure field π plays an important role in the regularity problem of MHD equations. We derive that the weak solution u , b is regular on 0 , T , which is provided for the scalar pressure field π in the Besov spaces.

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